There are 4 US Post Offices in Greene County serving a total of 17,635 residents equating to 4,409 residents per post office. It's estimated that approximately 28,147 packages are handled across the 4 county post offices annually. Greenville, NC has no relation to Greene County, NC. For the neighboring county that Greenville is in, see Pitt County, North Carolina. Greene County is a county located in the U.S. state of North Carolina. As of the 2010 census, the population was 21,362. Its county seat is Snow Hill."